You seem to be shaky on your terminology; NP problems can be arbitrarily easy, and they are usually decision problems (which always have a unique solution, yes or no); read more at our reference questions. I assume you want NPO-hard problems with unique solutions?
–
Raphael♦Apr 23 '14 at 14:34

Yes, I was meaning NP complete or NP hard, or whatever that is not in P... Sorry and thanks to point out
–
MarcoApr 23 '14 at 20:59

We don't know if NP-complete problems are not in P...
–
Raphael♦Apr 23 '14 at 21:06

Or US, a different complexity class. (For UP machines, there is always at most one accepting path, for US there can be more than one but they only accept if there is exactly one.)
–
David EppsteinApr 23 '14 at 3:34